Field notes / Experiment guide
What does it cost to grow one more cell?
Territory growth combines time spent at the boundary with the chance of entering fresh ground once there. Which part varies with the rule?
New to these ants? Start here.
An ant moves on a grid of coloured squares. Each colour tells it to turn left (L) or right (R). It advances that square to the next colour, then steps forward. A rule such as RLR is the list of turns, starting at colour zero. On a blank grid the same rule always makes the same trajectory.
Territory means every cell visited so far. Its boundary consists of visited cells with an unvisited neighbour. A highway is a repeating pattern of motion that carries the ant away. A tether means repeated returns to a small home region.
Growing like the cube root of time means taking eight times as many steps to double a linear size. The rotor walker is a comparison model that follows and rotates arrows stored on cells. A seed makes a random starting pattern reproducible; the ant itself can still move deterministically.
We distinguish c, the chance of discovering a cell per boundary step, from kappa (κ), time at the boundary normalized by perimeter divided by area. Explaining their values is harder than using them to account for growth.
A closer look
The idea under test
Separating boundary occupation, entry probability and perimeter geometry should clarify the measured growth rate.
What we learned
Early rule letters strongly predict fresh-ground entry probability. Perimeter measurements also show substantial finite-time drift, making exact exponent claims premature.
What this leaves open
The growth decomposition is accounting. Reconstructing growth from its own factors is not an independent explanation of why those factors take their values.
Read the evidence and reproduction recipe ↗
Inside the experiment
Methods, registered predictions, exact commands and saved analysis. These are the working research documents; expand them for the detail behind the introduction.
Methods and original experiment record
edge-statistics
Migrated legacy investigation (2026-10-14). Its files used to sit in the flat data/ directory (and calib/, occ/, snaps/, dumps*, knock* where listed) with the label prefix below; experiments/_migration/map.tsv gives the exact old -> new path of every file. This stub was generated from file names and script docstrings. It is not the original write-up: the question, timestamped hypotheses, commands and results are in notes/ (mainly notes/frontier-results.md, notes/frontier-status.md, notes/research-frontier*.md; search for the label), and the producing command is usually in the script docstring or a run_*.sh here.
Old labels / prefixes: edge, edgestats
Scripts
scripts/edge_exponent.py: Item 8: is the perimeter-vs-area exponent beta (finite-window 0.52) a finite-time effect that
Results
6 entries in results/ (0 are .log/.done markers); csv/json/txt outputs, *_stats.txt hold the summaries quoted in the notes.
Addendum (2026-10-19)
results/edgestats_sample.csv was produced by examples/edgestats.rs with K = 23 (window (2^22, 2^23], 4096 board), recovered by matching one rule's rows exactly; see experiments/2026-10-19-c-law-mechanism/results/PROVENANCE.md.
Notebook
No committed Jupyter notebook is available for this experiment yet.